As of October 7, Sony has dropped support for Facebook on PlayStation 4.
If you've had trouble sharing your screenshots, gameplay captures, or trophy unlocks to your feed, or your custom, Facebook-imported avatar isn't working on PlayStation Network anymore, that's why.
Everything to do with Facebook integration – including the ability to import friends from the social network – has been stripped away from the PS4's built-in share feature. This development is no doubt due to ongoing concerns over Facebook's use of personal data and the company's ensuing API changes.
I'm not sad to see this happen to Facebook, but I am ever so slightly affected. I used to privately upload my screens (say, for a guide or a review) to Facebook for easy access on my PC. I'm terrible at keeping track of flash drives – you can never have enough of 'em! – and that method was a time-saver.
If you now need an alternate way to upload a custom profile pic, you can do so via the PlayStation app.
Removal of Facebook Integration on PS4 [PlayStation]